What is the general solution for sin(x)+cos(x)-1=0 ?

The general solution for sin(x)+cos(x)-1=0 is x=2pin,x=2pin+pi/2

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sin(x)+cos(x)-1=0

sin (x) + cos (x) - 1 = 0

x = 2 πn, x = 2 πn + \frac{π}{2}

Solution steps

sin (x) + cos (x) - 1 = 0

Rewrite using trig identities

- 1 + 2 sin (x + \frac{π}{4}) = 0

Move

1

to the right side

2 sin (x + \frac{π}{4}) = 1

Divide both sides by

2

sin (x + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (x + \frac{π}{4}) = \frac{2}{2}

x + \frac{π}{4} = \frac{π}{4} + 2 πn, x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

Solve

x + \frac{π}{4} = \frac{π}{4} + 2 πn : x = 2 πn

Solve

x + \frac{π}{4} = \frac{3 π}{4} + 2 πn : x = 2 πn + \frac{π}{2}

x = 2 πn, x = 2 πn + \frac{π}{2}

tan (θ) = - 9

tan (θ) = 13

tan (θ) = 16

cos (θ) = - \frac{1}{5}

sin (2 x) = \frac{- 1}{2}

What is the general solution for sin(x)+cos(x)-1=0 ?
The general solution for sin(x)+cos(x)-1=0 is x=2pin,x=2pin+pi/2